77 research outputs found
Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
Results on the Prandtl-Blasius type kinetic and thermal boundary layer
thicknesses in turbulent Rayleigh-B\'enard convection in a broad range of
Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary
layer equations, we calculate the ratio of the thermal and kinetic boundary
layer thicknesses, which depends on the Prandtl number Pr only. It is
approximated as for and as for
, with . Comparison of the Prandtl--Blasius velocity
boundary layer thickness with that evaluated in the direct numerical
simulations by Stevens, Verzicco, and Lohse (J. Fluid Mech. 643, 495 (2010))
gives very good agreement. Based on the Prandtl--Blasius type considerations,
we derive a lower-bound estimate for the minimum number of the computational
mesh nodes, required to conduct accurate numerical simulations of moderately
high (boundary layer dominated) turbulent Rayleigh-B\'enard convection, in the
thermal and kinetic boundary layers close to bottom and top plates. It is shown
that the number of required nodes within each boundary layer depends on Nu and
Pr and grows with the Rayleigh number Ra not slower than \sim\Ra^{0.15}. This
estimate agrees excellently with empirical results, which were based on the
convergence of the Nusselt number in numerical simulations
Flow of foam through a convergent channel
International audienceWe study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events
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